Hold down Shift+Ctrl and click with the Eraser (Shift+Option on the Mac)

Push/Pull and Offset

Make a copy of the face you’re push/pulling

Press Ctrl (Option on the Mac) and use the Push/Pull tool

Repeat the last distance you push/pulled

Double-click a face with the Push/Pull tool

Repeat the last distance you Offset

Double-click a face with the Offset tool

Scale with the Scale tool

Scale about the center

Hold down Ctrl (Option on the Mac) while scaling

Scale uniformly (don’t distort)

Hold down Shift while scaling

Scale by a certain factor

Type a number and press Enter

Make something a certain size

Type the size and the units and then press Enter

Apply materials with the Paint Bucket tool

Sample a material from a face

Hold down Alt (Command on the Mac) and click the face with the tool

Paint all faces that match the one you click

Hold down Shift while you click

Create guides

Tell the Tape Measure or Protractor tool to create a guide

Press Ctrl (Option on the Mac) and click with the tool

Walk around your model with the Walk tool

Walk through things

Hold down Alt (Command on the Mac)

Run instead of walk

Hold down Ctrl (Option on the Mac)

Get taller or shorter instead of walking

Hold down Shift

Change your eye height

Select the Look Around tool, type a height, and press Enter

Change your field of view

Select the Zoom tool, type a number, type deg, and press Enter

STL import

When you are in the Import window, click the Options button and check-mark the Merge Coplanar Faces box. This will eliminate a lot of them lines from the start.
If you import a tiny object it will have some faces too small for SketchUp and your geometry will not be watertight. To fix that, restart the Import and go back in the Options menu and set the Units to the next bigger digit. Ex: If it's mm than import in cm, you'll know to group and scale down to 0.1 after.
Cheers!